Abstract
We study the probability distribution of the ground-state energy E in various Ising spin glasses. In most models, seems to become Gaussian with a variance growing as the system’s volume V. Exceptions include the Sherrington-Kirkpatrick model (where the variance grows more slowly, perhaps as the square root of the volume), and mean-field diluted spin glasses having couplings. We also find that the corrections to the extensive part of the disorder averaged energy grow as a power of the system size; for finite-dimensional lattices, this exponent is equal, within numerical precision, to the domain-wall exponent We also show how a systematic expansion of in powers of can be obtained for Migdal-Kadanoff lattices. Some physical arguments are given to rationalize our findings.
- Received 6 December 2002
DOI:https://doi.org/10.1103/PhysRevB.68.224404
©2003 American Physical Society